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Modelling turbulence generation in solitary waves on shear shallow water flows

Published online by Cambridge University Press:  14 May 2015

G. L. Richard  and
S. L. Gavrilyuk
G. L. Richard
Affiliation:
Université de Toulouse, Université Toulouse III Paul Sabatier, UMR CNRS 5219, IMT, 118 route de Narbonne, 31062 Toulouse CEDEX 9, France
S. L. Gavrilyuk*
Affiliation:
Aix-Marseille Université, UMR CNRS 7343, IUSTI, 5 rue E. Fermi, 13453 Marseille CEDEX 13, France Novosibirsk State University, 2 Pirogova 630090 Novosibirsk, Russia
*
†Email address for correspondence: sergey.gavrilyuk@univ-amu.fr
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Abstract

We derive a dispersive model of shear shallow water flows which takes into account a non-uniform horizontal velocity. This model generalizes the Green–Naghdi model to the case of shear flows. Besides the classical dispersion term in the Green–Naghdi model related to the acceleration of the free surface, it also contains a new dispersion parameter related to the flow structure. This parameter is related to the second moment of the velocity fluctuation with respect to the vertical coordinate. The distinction between shearing and turbulence based on the scale of variation of the velocity fluctuation is proposed. In particular, an equation for the turbulence generation is derived. Solitary waves for this model are obtained in explicit form. Comparison of solitary wave profiles with experimental ones is also performed. The agreement is very good apart from the small region near the top of the wave.

JFM classification

Geophysical and Geological Flows: Shallow water flows Waves/Free-surface Flows: Shear waves Waves/Free-surface Flows: Surface gravity waves

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Papers
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Journal of Fluid Mechanics , Volume 773 , 25 June 2015 , pp. 49 - 74
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© 2015 Cambridge University Press 

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